表面张力的斯特凡问题:径向对称下物理解的唯一性

IF 2.6 1区 数学 Q1 MATHEMATICS, APPLIED
Yucheng Guo, Sergey Nadtochiy, Mykhaylo Shkolnikov
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引用次数: 0

摘要

我们研究的是具有表面张力和径向对称初始数据的斯特凡问题。在此背景下,最近在 [21] 中提出了所谓物理解的概念,尽管熔化率固有膨胀,但物理解在全局上是存在的。本文致力于证明物理解是唯一的,这是自由边界不平坦或存在两相时的第一个此类结果。主要论证依赖于对三维布朗运动命中概率的详细分析,以及通过比较技术获得的自由边界的新颖凸性属性。在证明过程中,我们为自由边界和温度函数建立了多种正则性估计,这些估计本身就很有意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stefan Problem with Surface Tension: Uniqueness of Physical Solutions under Radial Symmetry

We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite the inherent blow-ups of the melting rate, has been recently introduced in [21]. The paper in hand is devoted to the proof that the physical solution is unique, the first such result when the free boundary is not flat, or when two phases are present. The main argument relies on a detailed analysis of the hitting probabilities for a three-dimensional Brownian motion, as well as on a novel convexity property of the free boundary obtained by comparison techniques. In the course of the proof, we establish a wide variety of regularity estimates for the free boundary and for the temperature function, of interest in their own right.

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来源期刊
CiteScore
5.10
自引率
8.00%
发文量
98
审稿时长
4-8 weeks
期刊介绍: The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
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